Example 2.1.1: Magnitude and unit vector

By (2.1.2),

By (2.1.3) the unit vector is the vector divided by this number:

$(\frac{4}{9}{)}^2+(\frac{4}{9}{)}^2+(\frac{7}{9}{)}^2=\frac{16+16+49}{81}=1$, as it must be for a unit vector. Note that $a_A$ has the same signs of components as $A$: normalising never changes direction.